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CATEGORIES:SEEMOD Workshop 9
SUMMARY:An effective criterion for periodicity of l-adic c
ontinued fractions - Laura Capuano (Oxford)
DTSTART;TZID=Europe/London:20190517T160000
DTEND;TZID=Europe/London:20190517T165000
UID:TALK125173AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/125173
DESCRIPTION:It goes back to Lagrange that a real quadratic irr
ational has always a periodic continued fraction.
Starting from decades ago\, several authors propos
ed different definitions of a l-adic continued fra
ction\, and the definition depends on the chosen s
ystem of residues mod l. It turns out that the the
ory of l-adic continued fractions has many differe
nces with respect to the real case\; in particular
\, no analogue of Lagrange’s theorem holds\, and t
he problem of deciding whether the continued fract
ion is periodic or not seemed to be not known. In
recent work with F. Veneziano and U. Zannier we in
vestigated the expansion of quadratic irrationals\
, for the l-adic continued fractions introduced by
Ruban\, giving an effective criterion to establis
h the possible periodicity of the expansion. This
criterion\, somewhat surprisingly\, depends on the
“real” value of the l-adic continued fraction.
LOCATION:MR3 Centre for Mathematical Sciences\, level -1
CONTACT:HoD Secretary\, DPMMS
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